A=number of seats in section A
B=number of seats in section B
C=number of seats in section C
We can suggest this system of equations:
A+B+C=55,000
A=B+C ⇒A-B-C=0
28A+16B+12C=1,158,000
We solve this system of equations by Gauss Method.
1 1 1 55,000
1 -1 -1 0
28 16 12 1,158,000
1 1 1 55,000
0 -2 -2 -55,000 (R₂-R₁)
0 12 16 382,000 (28R₁-R₂)
1 1 1 55,000
0 -2 -2 -55,000
0 0 4 52,000 (6R₂+R₃)
Therefore:
4C=52,000
C=52,000/4
C=13,000
-2B-2(13,000)=-55,000
-2B-26,000=-55,000
-2B=-55,000+26,000
-2B=-29,000
B=-29,000 / -2
B=14,500.
A + 14,500+13,000=55,000
A+27,500=55,000
A=55,000-27,500
A=27,500.
Answer: there are 27,500 seats in section A, 14,500 seats in section B and 13,000 seats in section C.
Answer:
20 ft long; 12 ft wide
Step-by-step explanation:
Let w = the width of the garden
Then l = w + 8
A = lw
A = (w + 8)w
=====
The sidewalk is 4 ft wide, so, for the big rectangle consisting of garden plus sidewalk:
Width = w +8
Length = w + 16
Area = (w + 8)(w + 16)
=====
The <em>difference</em> between the two areas is the area of the sidewalk (320 ft²).
(w + 8)(w + 16) - (w + 8)w = 320 Factor out w + 8
(w+ 8)(w + 16 – w) = 320 Combine like terms
(w+ 8) × 16 = 320 Divide each side by 16
w + 8 = 20 Subtract 8 from each side
w = 12 ft
l = 12 + 8
l = 20 ft
The garden is 20 ft long by 12 ft wide.
Answer:
4 kilometers
Step-by-step explanation:
<em>First! Let's create an equation, with our variable (x) representing the number of additional fifth kilometers Dan can afford. </em>
2 + 0.40x = 9.60
<em>Now, we have to solve for our x value by subtracting 2 from both sides.</em>
0.40x = 7.60
<em>Next, we can divide both sides by 0.40 to find out what our x value is equal too.</em>
x = 19
<em>Don't forget this x value is just for the number of </em><em>additional</em><em> fifth kilometers Dan can afford on top of his first fifth mile.</em>
<em />
<em>So! Dan can afford 20 fifth kilometers, which in turn in is 4 kilometers in total. </em>
<em />
Hope this Helps! :)
<em>Have any questions? Ask below in the comments and I will try my best to answer.</em>
-SGO
Answer:
1) 37
2) 23
3) 4
4) 58
5) 67
6) 7
7) x = 14
BC = 27
CD = 61
BD = 88
Step-by-step explanation:
1) Add them
2) Subtract them
3) Add them and set equal to 36
6x + 1 + x + 7 = 36
4) Add them and set equal to 9x - 39
47 + 3x + 10 = 9x - 39
Substitute x into 3x + 10 to find EF
5) Add them and set equal to 6x - 35
19 + 4x - 20 = 6x - 35
Substitute x into 6x - 35 to find UW
6) Add them and set equal to 7x-27
3x - 5 + x - 1 = 7x - 27
7) Add them. Solve for x and substitute.
4x - 29 + 5x - 9 = 7x - 10
